One important objective of the paper-making process is to maintain uniform consistency of the stock output as it progresses to drying and rolling. A diagram of the thick stock consistency dilution control system is shown in Figure P4.11(a). The amount of water added determines the consistency. The block diagram of the system is shown in Figure P4.11(b). Let H(s) = 1 and

Determine
(a) The closed-loop transfer function T(s) = Y(s)/R(s),
(b) The sensitivity STK, and
(c) The steady-state error for a step change in the desired consistency R(s) = A/s.
(d) Calculate the value of K required for an allowable steady-state error of 2%.
Figure P4.11
Paper-making control.

8 IG(s) 3s 1 Water Desired consistencyR(s) 7 Uls M Consistency Valve Controller_ measurement Pulp mixing To paper making U(s) His) Mis)